{"id":"https://openalex.org/W3106801134","doi":"https://doi.org/10.1145/3457341.3457346","title":"Exploiting symmetry in the power flow equations using monodromy","display_name":"Exploiting symmetry in the power flow equations using monodromy","publication_year":2020,"publication_date":"2020-09-01","ids":{"openalex":"https://openalex.org/W3106801134","doi":"https://doi.org/10.1145/3457341.3457346","mag":"3106801134"},"language":"en","primary_location":{"id":"doi:10.1145/3457341.3457346","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3457341.3457346","pdf_url":null,"source":{"id":"https://openalex.org/S176185422","display_name":"ACM communications in computer algebra","issn_l":"1932-2232","issn":["1932-2232","1932-2240"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320725","host_organization_name":"SIGSAM","host_organization_lineage":["https://openalex.org/P4310320725"],"host_organization_lineage_names":["SIGSAM"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Communications in Computer Algebra","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2011.14977","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055721131","display_name":"Julia Lindberg","orcid":"https://orcid.org/0000-0002-6840-6053"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Julia Lindberg","raw_affiliation_strings":["University of Wisconsin-Madison","University of Wisconsin-Madison, #TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Wisconsin-Madison","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"University of Wisconsin-Madison, #TAB#","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069834567","display_name":"Nigel Boston","orcid":"https://orcid.org/0000-0002-2807-4963"},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nigel Boston","raw_affiliation_strings":["University of Wisconsin-Madison","University of Wisconsin-Madison, #TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Wisconsin-Madison","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"University of Wisconsin-Madison, #TAB#","institution_ids":["https://openalex.org/I135310074"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110239075","display_name":"Bernard C. Lesieutre","orcid":null},"institutions":[{"id":"https://openalex.org/I135310074","display_name":"University of Wisconsin\u2013Madison","ror":"https://ror.org/01y2jtd41","country_code":"US","type":"education","lineage":["https://openalex.org/I135310074"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bernard C. Lesieutre","raw_affiliation_strings":["University of Wisconsin-Madison","University of Wisconsin-Madison, #TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Wisconsin-Madison","institution_ids":["https://openalex.org/I135310074"]},{"raw_affiliation_string":"University of Wisconsin-Madison, #TAB#","institution_ids":["https://openalex.org/I135310074"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I135310074"],"apc_list":null,"apc_paid":null,"fwci":0.1268,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.54254792,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"54","issue":"3","first_page":"100","last_page":"104"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9761999845504761,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9761999845504761,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11673","display_name":"Advanced Topics in Algebra","score":0.9487000107765198,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/monodromy","display_name":"Monodromy","score":0.9425204992294312},{"id":"https://openalex.org/keywords/subvariety","display_name":"Subvariety","score":0.77040696144104},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7054912447929382},{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.6573163270950317},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.6379048824310303},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.6083084344863892},{"id":"https://openalex.org/keywords/homogeneous-space","display_name":"Homogeneous space","score":0.5490192174911499},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.4856806993484497},{"id":"https://openalex.org/keywords/homotopy-analysis-method","display_name":"Homotopy analysis method","score":0.4837941825389862},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.435624361038208},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.4121694266796112},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4094636142253876},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09337565302848816},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08813753724098206}],"concepts":[{"id":"https://openalex.org/C96403706","wikidata":"https://www.wikidata.org/wiki/Q543956","display_name":"Monodromy","level":2,"score":0.9425204992294312},{"id":"https://openalex.org/C2777183706","wikidata":"https://www.wikidata.org/wiki/Q630771","display_name":"Subvariety","level":3,"score":0.77040696144104},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7054912447929382},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.6573163270950317},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.6379048824310303},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.6083084344863892},{"id":"https://openalex.org/C96469262","wikidata":"https://www.wikidata.org/wiki/Q1324364","display_name":"Homogeneous space","level":2,"score":0.5490192174911499},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.4856806993484497},{"id":"https://openalex.org/C173636693","wikidata":"https://www.wikidata.org/wiki/Q17030668","display_name":"Homotopy analysis method","level":3,"score":0.4837941825389862},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.435624361038208},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.4121694266796112},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4094636142253876},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09337565302848816},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08813753724098206},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/3457341.3457346","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3457341.3457346","pdf_url":null,"source":{"id":"https://openalex.org/S176185422","display_name":"ACM communications in computer algebra","issn_l":"1932-2232","issn":["1932-2232","1932-2240"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320725","host_organization_name":"SIGSAM","host_organization_lineage":["https://openalex.org/P4310320725"],"host_organization_lineage_names":["SIGSAM"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Communications in Computer Algebra","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2011.14977","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.14977","pdf_url":"https://arxiv.org/pdf/2011.14977","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:3106801134","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/2011.14977.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2011.14977","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2011.14977","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2011.14977","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.14977","pdf_url":"https://arxiv.org/pdf/2011.14977","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3106801134.pdf","grobid_xml":"https://content.openalex.org/works/W3106801134.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W2240778849","https://openalex.org/W2560903687","https://openalex.org/W2783504746","https://openalex.org/W2799440847","https://openalex.org/W2806263336","https://openalex.org/W2914261292","https://openalex.org/W2963196299","https://openalex.org/W2963247163","https://openalex.org/W2963422512","https://openalex.org/W2963442161","https://openalex.org/W2963709552","https://openalex.org/W2993485388"],"related_works":["https://openalex.org/W3136046648","https://openalex.org/W2520285876","https://openalex.org/W3126038125","https://openalex.org/W2962778504","https://openalex.org/W3197590657","https://openalex.org/W1596283011","https://openalex.org/W2174122123","https://openalex.org/W2949121158","https://openalex.org/W2056767438","https://openalex.org/W3091792173","https://openalex.org/W3195119794","https://openalex.org/W2951512590","https://openalex.org/W2304036893","https://openalex.org/W2950272280","https://openalex.org/W2963999906","https://openalex.org/W2963039554","https://openalex.org/W333034333","https://openalex.org/W3103585951","https://openalex.org/W2761988881","https://openalex.org/W2188148500"],"abstract_inverted_index":{"We":[0,9,28,36],"propose":[1],"solving":[2],"the":[3,11,23,34,65,85],"power":[4,66,86],"flow":[5,67,87],"equations":[6,88],"using":[7,69],"monodromy.":[8],"prove":[10],"variety":[12],"under":[13],"consideration":[14],"decomposes":[15],"into":[16],"trivial":[17],"and":[18,21,46,51],"nontrivial":[19,24],"subvarieties":[20],"that":[22,80],"subvariety":[25],"is":[26,94],"irreducible.":[27],"also":[29],"show":[30],"various":[31],"symmetries":[32],"in":[33],"solutions.":[35],"finish":[37],"by":[38],"giving":[39,52],"numerical":[40],"results":[41],"comparing":[42],"monodromy":[43,70],"against":[44],"polyhedral":[45],"total":[47],"degree":[48],"homotopy":[49,73],"methods":[50],"an":[53],"example":[54],"of":[55,91],"a":[56],"network":[57],"where":[58,71],"we":[59],"can":[60],"find":[61],"all":[62,82],"solutions":[63,83],"to":[64,84],"equation":[68],"other":[72],"techniques":[74],"fail.":[75],"This":[76],"work":[77],"gives":[78],"hope":[79],"finding":[81],"for":[89],"networks":[90],"realistic":[92],"size":[93],"possible.":[95]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}
